# Lesson 3: Compound Probability

**STANDARDS (CCSS AND NCTM)**

**Grade 7:**Statistics and Probability (**CCSS**7.SP.8)**Grades 6–8:**Construct Viable Arguments & Model with Mathematics (**CCSS**MP3 and 4)**NCTM:**Data Analysis and Probability

**OBJECTIVE**

- Students will use a tree diagram to derive the formula for compound probability; and
- Students will use the formula for compound probability to calculate the probability of multiple independent events.

**MATERIALS**

- one coin (for demonstration)
- Worksheet 3 Printable (PDF): "Math Masters"
- Bonus Worksheet Printable (PDF): "Mind Your Own Business!"
- Resource: Worksheet Answer Key (PDF)
- Resource: Mini-Poster (PDF)
- Resource: Standards Alignment Chart (PDF)
- Bonus Activity: Online Probability Challenge

Click for *whiteboard-ready printables*.

**DIRECTIONS**

**Introduction to Compound Probability**

1. Show the coin to the class and ask what is the probability of the coin landing on heads.

2. Recall the work done in Lesson 1 on tree diagrams and ask for a volunteer to explain how all the outcomes for three flips in a row could be depicted.

3. Ask what the probability of a coin landing on heads three times in a row would be. Walk the students through a tree diagram to demonstrate that there is one outcome for three heads in a row while there are seven unfavorable outcomes (HHT, HTT, HTH, TTT, TTH, THT, THH), so the probability is one out of eight or 1/8 or 12.5%.

4. Ask if there is a way to calculate the probability of tossing three heads in a row without setting up the tree diagram. If necessary, point out that the probability of one heads flip is 1/2 or 50% or .5 and, for three heads in a row:

1/2 x 1/2 x 1/2 = 1/8 *or*

.5 x .5 x .5 = .125 *or*

50% (.5) x 50% (.5) x 50% (.5) = 12.5% or .125

5. **Guided Practice: **Individually or in pairs, ask students, using both the formula and a tree diagram, to determine:

- The probability of rain in both Chicago and San Francisco on the same day if the probability of rain is 20% in Chicago and 50% in San Francisco (20% x 50% = 10%)
- The probability of a six-sided die landing on an even number then flipping heads (50% x 50% = 25%)

Ask students to explain their answers to the class.

7. Distribute Worksheet 3. Read the introduction and review the facts with the class. Ask students to complete the worksheet. Review answers as a class. Worksheet Answer Key (PDF). As a bonus activity, have students complete the Bonus Worksheet.**LESSON EXTENSION**

Have students use the Online Probability Challenge to practice using probability skills for real-life purposes. This interactive online activity challenges students to use probability to help Rick and Athena plan a summer concert tour. This activity can be used as an in-class lesson activity or an out-of-the classroom extension.